61.6 Solving linear diophantine equations using matrices

Extract

The method described in this note is, like other standard approaches, based on the “Euclidean algorithm”, but a matrix format is used (assuming the coefficients have no common factor) to reduce the equation ax + by = c to a form such as

or a similar equation with matrix (k l),(k −l) or (−1 k). The following lemma is easily verified.